Typically, a hybrid electric vehicle (HEV) can be equipped with one or more electric motors (EM) powered by one or more electric power sources, e.g., batteries and fuel cells, etc., and an internal combustion engine (ICE) powered by fuel, e.g., gasoline, diesel fuel, etc, HEV are energy-efficient, cost-effective, and dependable. This is mainly due to the ability of the EM to regenerate energy during braking, which would otherwise be lost, and to store that energy into relatively less expensive batteries than the type of batteries installed in purely electrical vehicles, while also having the advantage of a long range, high reliability, and high energy density of the ICE.
For the HEV, an important question is when to use the EM or the ICE. It is known that the overall energy efficiency of the HEV can be improved significantly when the operation of the ICE and EM is coordinated carefully by taking into consideration the route the vehicle travels, e.g., geography, altitude, etc., and the conditions of the vehicle, e.g., velocity and state of charge (SoC) of the electric sources.
In such cases, it is necessary to select the source of motive power for the HEV. Typically, the ICE and EM have different efficiencies of converting electric or chemical energy into mechanical energy, which depends on the current driving conditions, such as speed, road inclination, required acceleration, etc. In addition, the decisions have to be made over a time horizon spanning an entire duration of a vehicle trip as depending on the conditions of the road and the vehicle.
For example, it may be more advantageous to conserve electric energy at a current time, and use the electric energy later, or vice versa. The necessity to make decisions for many points along the route makes this problem a hard combinatorial problem that requires computational resources far exceeding those available in computers onboard currently available in HEV.
Some example prior art methods that considered this issue include Ngo et al., “An optimal control-based algorithm for hybrid electric vehicle using preview route information,” American Control Conference (ACC), 2010; V. Larsson, L. Johannesson, B. Egardt, and A. Lassson, “Benefit of route recognition in energy management of plug-in hybrid electric vehicles,” American Control Conference (ACC), 2012; V. Larsson, L. Johannesson, and B. Egardt, “Cubic spline approximations of the dynamic programming cost-to-go in HEV energy management problems,” European Control Conference (ECC), 2014; V. Larsson, L. Johannesson, B. Egardt, and S. Karlsson, “Commuter route optimized energy management of hybrid electric vehicles,” IEEE Transactions on Intelligent Transportation Systems, Vol. 15, No. 3, 2014, pp. 1-10; V. Larsson, L. Johannesson, and B. Egardt. “Analytic solutions to the dynamic programming sub-problem in hybrid vehicle energy management,” IEEE Transactions on Vehicular Technology, 2014.
U.S. Pat. No. 8,612,077 uses a Receding Horizon Control with a dynamic programming (DP) on a shorter than the original horizon. Instead of planning for all time steps, that method plans for a relatively short time horizon. The idea is to construct a smaller set of virtual segments from the original segments. In the set of virtual segments, all except the last are the same as the original segment starting from the vehicle's current segment. The last virtual segment, however, is a summary of the remaining original segments, and is characterized by the total length of segments left, the average speed of the vehicle, and the average grade of the remaining route segments. DP is applied to this set of virtual segments.
Most prior art solutions use fundamental optimization methods, such as dynamic programming or convex optimization to arrive at an optimal or close to optimal control policy for the two motors of an HEV. Savings in the amount of up to 17% have been estimated to be possible, see V. Larsson, L. Johannesson, and B. Egardt. “Analytic Solutions to the Dynamic Programming sub-problem in Hybrid Vehicle Energy Management,” IEEE Transactions on Vehicular Technology, 2014.
Although true optimality is a very favorable feature of those methods, their computational complexity precludes the use of current embedded computational devices available in mass-produced vehicles. Furthermore, meticulous computation of the truly optimal control policy might not be necessary or even very accurate in light of the significant uncertainty in the driving conditions and energy consumption of the vehicle. For this reason, it is highly desirable to find computational methods that can approximate the optimal control policy and achieve most of the possible savings at a much lower computational cost. This allows deployment of methods on embedded devices comparable in computational speed to those currently used in engine control units (ECU).
A lower computational cost can be achieved when a much smaller optimization problem is solved in real time. Ideally, this problem should involve only variables and data pertaining to the current moment in time, or at most the immediately following decision periods. One example of such an approach is an equivalent consumption minimization strategy (ECMS). That strategy is based on the insight that whereas the cost of fuel is constant and known during the entire duration of the trip, the relative value of the electrical charge in the vehicle's battery is typically strongly time- and position-dependent. (If that was not the case, then the optimal policy would be trivial, that is, to always use the engine that is less expensive to operate, until its source of energy is completely depleted.) So, if the relative value of electrical charge can be estimated or approximated at all times, then a fast static optimization over only the current moment of time would be sufficient. The success of that approach depends on how accurately this relative value can be approximated.
The hybrid vehicle optimization problem can be formulated as an optimal control problem over a planning horizon of length Tf, where the only dynamic state variable x(t) represents the state of charge (SoC) of the battery, usually normalized with respect to the battery capacity, such that x(t)ε[0,1] is non-dimensional. The control signal a(t) can be either discrete or continuous. In its simplest form, it is binary: a(t)ε{0,1}, where a(t)=0 represents a decision to use the electric motor (EM) at time t, and a(t)=1 represents the decision to use the ICE.
A more detailed control includes a choice of gear for the ICE. So for example, if a(t)ε{0,1, 2, 3, 4, 5}, the choice of a(t)=4 signifies using the ICE in the fourth gear. An even more detailed control can consist of the power split ratio ξ(t)ε[0,1] between the EM and ICE. In such a case, the variable ξ(t) is usually again discretized into a set of integer values a(t), at the desired resolution. One exception is V. Larsson, L. Johannesson, and B. Egardt. “Analytic Solutions to the Dynamic Programming sub-problem in Hybrid Vehicle Energy Management,” IEEE Transactions on Vehicular Technology, 2014).
The run-curve of the vehicle, which is the altitude profile of the route and the speed of the vehicle along the route, is assumed to be fixed and known in advance.
In practice, the run-curve is determined by the selected route and the speed constraints along the route. Under this assumption, the system dynamics, e.g., battery charging and discharging, is described by a function{dot over (x)}(t)=g(x(t),a(t),t),where g denotes the dependency of the rate of change of the SoC on its current level and the selected source of power.
In general, the function is time and position variant: when the slope of the road is steeper, and the EM is used, more electrical energy is expended to follow the run-curve. Conversely, when the vehicle is moving downhill, less electrical energy is expended, and when regenerative brakes are used, the change in the state of charge can be positive.
The objective of the vehicle energy management system for the HEV is to minimize the total energy consumption
            J      *        =                  min                  a          ⁡                      (            ·            )                              ⁢              {                              c            ⁡                          (                              x                ⁡                                  (                                      T                    f                                    )                                            )                                +                                    ∫              0                              T                f                                      ⁢                                          c                ⁡                                  (                                                            x                      ⁡                                              (                        t                        )                                                              ,                                          a                      ⁡                                              (                        t                        )                                                              ,                    t                                    )                                            ⁢                              ⅆ                t                                                    }              ,where a(·) is the control signal over the entire optimization period, c(x(t), a(t), t) is the immediate cost of fuel (also time and position dependent), and c(x(T)) is the terminal cost expressing a penalty for leaving the battery less full than at the starting time x(0), or a bonus for leaving it more charged. The running cost c(x(t), a(t), t) can be obtained either by means of a vehicle simulator, or estimated from recorded vehicle performance data during actual operation of the vehicle. Typically, the terminal cost for the final state c(x(Tf)) is a linear or quadratic function of a difference in the state of charge between last and first statex(Tf)−x(0), e.g., c(x(T))=w1(x(Tf)−x(0))for some constant w1>0.
This optimization is subject to constraints on the state variables, for example x(t) can be limited to be between 20%, and 80% of the maximum charge, in order to avoid damage to the battery.
Many solution methods to the hybrid vehicle optimization problem are known: A. Sciarretta and L. Guzzella, “Control of hybrid electric vehicles,” IEEE Control Systems Magazine, 2007). Several principal approaches can be identified:
Dynamic Programming (DP)
A general approach is to use Dynamic Programming (DP). DP starts from discretizing time with a suitable discretization time step Δt. The result would be T=Tf/Δt time steps. Then, the goal is to minimize the following cost function:
      J    *    =            min              a        ⁡                  (          t          )                      ⁢                  {                              c            ⁡                          (                              x                ⁡                                  (                  T                  )                                            )                                +                                    ∑                              t                =                1                                            T                -                1                                      ⁢                          c              ⁡                              (                                                      x                    ⁡                                          (                      t                      )                                                        ,                                      a                    ⁡                                          (                      t                      )                                                        ,                  t                                )                                                    }            .      
It is known that one can solve this optimization problem using DP, e.g., V. Larsson, L. Johannesson, and B. Egardt, “Cubic spline approximations of the Dynamic Programming cost-to-go in HEV energy management problems,” European Control Conference (ECC), 2014).
The optimal value function Vt(x(t)) can be defined as follows:
            V      t        ⁡          (              x        t            )        ⁢      =    Δ    ⁢      {                                                                      c                ⁡                                  (                                      x                    ⁡                                          (                      T                      )                                                        )                                                                                    t                =                T                                                                                                          min                  a                                ⁢                                  {                                                            c                      ⁡                                              (                                                                              x                            ⁡                                                          (                              t                              )                                                                                ⁢                          a                                                )                                                              +                                                                  V                                                  t                          +                          1                                                                    ⁡                                              (                                                  x                          ⁡                                                      (                                                          t                              +                              1                                                        )                                                                          )                                                                              }                                                                                    1                ≤                t                <                                  T                  ′                                                                    ⁢                                  ⁢        where        ⁢                                  ⁢                  x          ⁡                      (                          t              +              1                        )                              =                        f          ⁡                      (                                          x                ⁡                                  (                  t                  )                                            ,                              a                ⁡                                  (                  t                  )                                            ,              t                        )                          ⁢                  =          def                ⁢                              ∫                                                            T                  f                                                  Δ                  ⁢                                                                          ⁢                  t                                            ⁢                              (                                  t                  -                  1                                )                                                                                      T                  f                                                  Δ                  ⁢                                                                          ⁢                  t                                            ⁢              t                                ⁢                                    g              ⁡                              (                                                      x                    ⁡                                          (                      τ                      )                                                        ,                                      a                    ⁡                                          (                      t                      )                                                        ,                  τ                                )                                      ⁢                                          ⅆ                τ                            .                                          
These functions can be obtained by backward update, starting from time T and getting back to time t=1. Knowing the optimal value function is enough to determine the optimal controller.
There are two difficulties with this problem. The first is that when the number of time steps is very large, the computation time is high, and as a result, infeasible to be implemented on an onboard computer. The second problem is that because the state variable xt is continuous, one has to approximate the optimal value function. One approach is to discretize xt. For the HEV problem, discretization in the order of thousands of individual states for each time step is usually sufficient to get good results.
Equivalent Consumption Minimization Strategies (ECMS)
The idea of this approach is to turn the sequential dynamic problem into a static optimization problem, by assuming that there is an equivalent cost of using charge of the battery, and comparing this cost with the cost of fuel, so that the engine that is less expensive is used at a given decision period. This method is very practical and easy to implement in an onboard computer. However, its main shortcoming is the need to know the equivalent cost of electrical charge. If the cost is assumed to be constant, and is higher than that of fuel, then only the ICE is used.
This is far from optimal, because the benefits of the EM are ignored. Conversely, if the electric cost is lower than that of fuel, only the EM is used until the battery is depleted to the lowest level allowed. Afterwards the vehicle switches to ICE, and returns to the EM only when some power is regenerated. This can deplete the battery, so the vehicle has to rely only on the ICE for the remainder of the trip. Clearly, this is far from optimal. Nevertheless, this strategy can be advantageous when the efficiencies of the ICE and the EM are different for different operating regimes, for example low speed and high speed.